The impact of external market conditions on real options valuation

Transcription

1 The impact of external market conditions on real options valuation Marie Lambert a Manuel Moreno b Federico Platania c a HEC Liège, University of Liège b University of Castilla La-Mancha c Pôle Universitaire Léonard de Vinci March 26-27, th Financial Risks International Forum - Paris, France This project was supported by the FRS - FNRS under Grant T14.14.

2 How do macroeconomic or industry factors influence R&D project s 1 value (NPV) 2 success 3 failure... over time?

3 We present a novel valuation model based on real options 1 that incorporates the impact of external forces, such as market conditions, economic uncertainty, innovation, firm competition on the cash flow generation 2 that features an option to abandon 3 that enables to estimate the impact of these external conditions on the optimal launching time for the project as well as on success or failure rates of the project Our practical case covers a pharmaceutical R&D project, but the model and methodology can be easily extrapolated to any industry

4 The literature has shown the economic and social impact of R&D projects as well as the impact of the economic and social context on R&D spending International context, GDP as determinants of public spending in research and developments (Hammadou et al., 214, RP) Effect of public funding on innovative projects (Lanahan and Feldman, 217, RES) Productivity growth and R&D expenses (e.g. Kancs an Siliverstovs, 216, RP) Social and economic impact of R&D (e.g. Brautzsch et al., 215, RP; Ugur et al., 216, RP)

5 1 Literature Review Our contribution: modeling external forces Project s value 2 3

6 Literature Review Our contribution: modeling external forces Project s value

7 Theoretical framework Literature Review Our contribution: modeling external forces Project s value In the extant literature, real options have been used to model staged investments (e.g. Madj and Pindyck, 1987, JFE; Berk et al., 24, RFS) the optimal timing of investments (e.g. McDonald and Siegel, 1986, QJE; Posner and Zuckerman, 199, JAP) the impact of uncertainty in cash flows and cost on the project s value and risk (e.g. Schwartz, 24, EN; Berk et al., 24, RFS)

8 Theoretical framework Literature Review Our contribution: modeling external forces Project s value Modeling choices Modeling project s market value (e.g. Madj and Pindyck, 1987, JFE; Pennings and Sereno, 211, EJOR; Alexander et al., 212, EJOR) Modeling project s cash flows (e.g. Berk et al., 24, RFS; Schwartz, 24, EN) Modeling cost of completion and expenditures (e.g. DiMasi et al., 23, JHE; Pindyck, 1993, JFE; McDonald and Siegel,1986, QJE) Modeling technical risk (e.g. Schwartz, 24, EN ; Pindyck, 1993, JFE ; Pennings and Sereno, 211, EJOR)

9 Theoretical framework Literature Review Our contribution: modeling external forces Project s value In the literature, it is common to model the evolution of the project or the evolution of the cash flow as a stochastic differential equation... Geometric Brownian motion Arithmetic Brownian motion Ornstein-Uhlenbeck process dc t = µ(c, t)dt + σ(c, t)dw These models account for market uncertainty and idiosyncratic risk of the project but not for external cyclical forces

10 Theoretical framework Literature Review Our contribution: modeling external forces Project s value To account for technical risk, we generalize the Poisson distribution... Probability of success = e λ Probability of technical failure = λ k e λ =1 e λ k! k=1

11 Theoretical framework Literature Review Our contribution: modeling external forces Project s value The expected project value conditional to technical risk is given as E [V Technical Risk] = V (k =) e λ + V (k =1, 2,..., ) (1 e λ) Assuming V (k =1, 2,..., ) = During the development process the discount factor is given by e r d t = e (r+ˆλ)t

12 Theoretical framework Literature Review Our contribution: modeling external forces Project s value All these models share the same source of uncertainty... Arandomwalkweightedbyσ(C, t) forcapturingmarketand idiosyncratic risk APoissondistributiontoaccountfortechnicalrisk No model accounts for... Seasonal effects Business cycle Other relevant external forces

13 Economic and market external forces Literature Review Our contribution: modeling external forces Project s value Consider the net cash flow stream of a successful project C t = f (t)+y t Where dy t = µdt + σdw t Arithmetic Brownian motion f (t) = Fourier series The net cash flow of a successful project is given by an arithmetic Brownian motion process plus a time-dependent component depicted by a Fourier series. The Fourier series is a function defined as the sum of a set of simple sines and cosines, representing all the forces that impact the generation of cash flows.

14 Cash flow generation Literature Review Our contribution: modeling external forces Project s value Under the risk neutral probability P Q,thesolutionatanygiventimet is t Y t = Y e rt + σ C t = Y e rt + f (t)+σ e r(t s) dw Q s t e r(t s) dw Q s where Wt Q P Q. is a standard Wiener process under the risk-neutral measure

15 State vector Literature Review Our contribution: modeling external forces Project s value Let s define the economic state vector... Φ (j) with j N Each state...

16 State vector Literature Review Our contribution: modeling external forces Project s value Let s define the economic state vector... Φ (j) with j N Each state... corresponds to a specific scenario described by the cyclicality and the phase of the economic forces

17 Patent value Literature Review Our contribution: modeling external forces Project s value The expected patent value conditional to certain economic state is given as... E [ V Φ (j)] ( = V t, C t, I t ;Φ (j)) Pr (Φ =Φ (j))

18 Simulation exercise

19 Pharmaceutical project s stages Two major phases... 1 Research and development phase 2 Market phase The failure of one stage leads to overall project termination. We assume that once the project successfully passes every test and stage of the R&D process and finally achieves regulatory approval, technical risk virtually vanishes.

20 Economic forces For the sake of simplicity let s assume two economic forces... 1 US Gross domestic product (GDP) The business cycle is defined as the cyclical movement of the GDP around its long-term trend Hodrick-Prescott (1997) filter to disentangle the cyclical behaviour from the long-term trend 278 quarterly GDP observations ranging from January 1947 to April 216, obtained from the Federal Reserve Bank of St. Louis web page 2 VIX index Barometer of investor sentiment and market volatility Hodrick-Prescott (1997) filter , monthly observations provided by the Chicago Board Options Exchange (CBOE)

21 GDP cyclical component.5 GBP cyclical component /1947 7/1955 4/1964 1/1973 7/1981 4/199 1/1998 7/27 4/216 Time Power spectral density Frequency (Hz) Peak at a frequency of.1871hz Representing a cyclical period of 5.35 years

22 Volatility cycle 1 VIX cyclical component /199 4/1993 8/ /1999 3/23 7/26 1/29 2/213 6/216 Time.25 Power spectral density Frequency (Hz) VIX short- to medium-term cyclical component Two dominating peaks with period of 1.4 and 3.8 years

23 Volatility cycle.4 VIX demeaned long-term component /199 4/1993 8/ /1999 3/23 7/26 1/29 2/213 6/216 Time.25 Power spectral density Frequency (Hz) Volatility long-term component Representing a long term period of years (.755 Hz)

24 Amplitude parameter We use two well known Pharmaceutical Indexes: S&P 5 Pharmaceutical Index NYSE ARCA Pharmaceutical Index Ranging from July 1992 to April 216 S5PHAR Index DRG Index GDP cyclical component.497 (<.1).511 (<.1) VIX cyclical component.932 (.195).913 (.192) VIX long-term component.344 (<.1).3151 (<.1) R

25 Simulation exercise Project s net cash flow when launching at the peak of the cycle and entering into recession, that is φ = at the trough of the cycle and entering into the recovery phase, that is φ = π at an intermediate phase, φ = π/2

26 Simulation exercise - Business cycle Business cycle impact on the project s net cash flow is modeled as f (t) =1{.4959 cos ( t + φ 1 )}

27 Simulation exercise - Business cycle Conditional Expected Patent Value. Business cycle Business Cycle Panel Phase A B V (t, C t, I t ; φ 1 =) 98.7 (3.2) 64.1 (4.3) V (t, C t, I t ; φ 1 = π) (4.2) (4.4) V (t, C t, I t ; φ 1 = π/2) (3.9) (4.4) Table: This table presents the patent value conditional to the phase parameterin the business cycle. Panel A: With abandon option Panel B: Without abandon option

28 Simulation exercise - Business and volatility cycles Patent value π 3π/4 π/2 π/4 Volatility cycle phase π/4 π/2 Business cycle phase 3π/4 π 1

29 We perform a new exercise fitting the parameters of the fourier series to cash flow data of pharmaceutical firms active in anti-infective drug New external forces are assumed to better impact a specific pharmaceutical project Economic and political (business cycle and economic policy uncertainty index) Innovation (R&D expenditure as % of GDP, patent applications) Health expenditures (per capita, out of pocket) Competition (H concentration index based on sales)

30 New simulation exercise We consider the impact of these forces on a hypothetical project s success, abandon rate and value The project has an initial cash-flow of 1 M$ (5 M$ standard deviation) per quarter with an initial cost to completion equal to 1 M$ (sigma=.5) US versus Europe (EU) Big versus small caps

31 External forces Figure: Spectral analysis EU EPU.8 Cyclical component EPU in Europe /1987 4/199 8/ /1996 4/2 8/23 12/26 4/21 8/213 12/216 Time.5 Power spectral density Frequency (Hz)

32 External forces Figure: Spectral analysis US EPU.6 Cyclical component EPU in United States /1987 4/199 8/ /1996 4/2 8/23 12/26 4/21 8/213 12/216 Time.2 Power spectral density Frequency (Hz)

33 External forces Figure: Spectral analysis EU Concentration.4 Cyclical component concentration index in Europe Time.1 Power spectral density Frequency (Hz)

34 External forces Figure: Spectral analysis US concentration.1 Cyclical component concentration index in United States Time Power spectral density Frequency (Hz)

35 External forces Table: Cyclical components of external factors Panel: United States Angular Freq (ω) Frequency (f ) Period Economic Policy Uncertainty Gross Domestic Product Research and development expenditure (% of GDP) Patent applications Health expenditure per capita Out of pocket health expenditure Concentration

36 External forces Table: Cyclical components of external factors Panel: Europe Angular Freq (ω) Frequency (f ) Period Economic Policy Uncertainty Gross Domestic Product Research and development expenditure (% of GDP) Patent applications Health expenditure per capita Out of pocket health expenditure Concentration

37 Peer group analysis Table: CF structure - Descriptive Statistics Anti-infective Pharmaceutical Market EU: 13 US:6 Average quarterly Cash-Flow Standard Deviation Maximum Minimum Anti-infective EU Big-Cap: 3 Small-Cap:3 Average quarterly Cash-Flow Standard Deviation Maximum Minimum 11-44

38 Fitting forces to cash flow structure Table: Factors and amplitudes Panel: Anti-infective EU Market US Market Amplitude Phase Amplitude Phase Economic Policy Uncertainty 1(.11) (.1) Gross Domestic Product 14 (.8) (.1) Research and development expenditure (% of GDP) 18 (.9) (.1).8577 Patent applications 9(.1) (.4) Health expenditure per capita 47 (.1) (.1). Out of pocket health expenditure 17 (.3) (.5) Concentration 47 (.1) (.2) This table presents the standardized amplitude parameter (p-value) of each factor

39 Fitting forces to cash flow structure Table: Factors and amplitudes Panel: Europe Big Cap Small Cap Amplitude Phase Amplitude Phase Economic Policy Uncertainty 7(.1) (.37) Gross Domestic Product 1 (.14) (.11) Research and development expenditure (% of GDP) 18 (.5) (.19).288 Patent applications 15 (.1) (.22) Health expenditure per capita 17 (.1) (.1) Out of pocket health expenditure 16 (.16) (.16) Concentration 94 (.1) (.7) This table presents the standardized amplitude parameter (p-value) of each factor

40 Launching time in US Figure: All firms 5 Economic Policy Uncertainty 2 Gross Domestic Product -5 t = 1/217 t 1 = 1/218 t 2 = 1/219 1/212 1 Research and development expenditure -2 t = 1/217 t 1 = 1/218 t 2 = 1/219 1/212 5 Patent Application -1 t = 1/217 t 1 = 1/218 t 2 = 1/219 1/212-4 Health expenditure per capita -5 t = 1/217 t 1 = 1/218 t 2 = 1/219 1/212 5 Out of Pocket Health expenditure t = 1/217 t = 1/218 1 t = 1/ /212 1 Concentration -5 t = 1/217 t = 1/218 1 t = 1/ /212 5 t = 1/217 t 1 = 1/218 t 2 = 1/219 1/212

41 Launching time in EU Figure: All firms 1 Economic Policy Uncertainty 1 Gross Domestic Product -1 t = 1/217 t 1 = 1/218 t 2 = 1/219 1/212 1 Research and development expenditure -1 t = 1/217 t 1 = 1/218 t 2 = 1/219 1/212 1 Patent Application t = 1/217 t 1 = 1/218 t 2 = 1/219 1/212 5 Health expenditure per capita 4 t = 1/217 t 1 = 1/218 t 2 = 1/219 1/212 2 Out of Pocket Health expenditure t = 1/217 t = 1/218 1 t = 1/ /212 5 Concentration -2 t = 1/217 t = 1/218 1 t = 1/ /212-5 t = 1/217 t 1 = 1/218 t 2 = 1/219 1/212

42 Launching time in EU Figure: Big Caps EU 1 Economic Policy Uncertainty 1 Gross Domestic Product -1 t = 1/217 t 1 = 1/218 t 2 = 1/219 1/212 1 Research and development expenditure -1 t = 1/217 t 1 = 1/218 t 2 = 1/219 1/212-5 Patent Application t = 1/217 t 1 = 1/218 t 2 = 1/219 1/ Health expenditure per capita -15 t = 1/217 t 1 = 1/218 t 2 = 1/219 1/212 1 Out of Pocket Health expenditure 1 5 t = 1/217 t = 1/218 1 t = 1/ /212 5 Concentration -1 t = 1/217 t = 1/218 1 t = 1/ / t = 1/217 t 1 = 1/218 t 2 = 1/219 1/212

43 Launching time in EU Figure: Small Caps EU 1 Economic Policy Uncertainty 1 Gross Domestic Product -1 t = 1/217 t 1 = 1/218 t 2 = 1/219 1/212 1 Research and development expenditure -1 t = 1/217 t 1 = 1/218 t 2 = 1/219 1/212 1 Patent Application -1 t = 1/217 t 1 = 1/218 t 2 = 1/219 1/212-5 Health expenditure per capita -1 t = 1/217 t 1 = 1/218 t 2 = 1/219 1/212 1 Out of Pocket Health expenditure t = 1/217 t = 1/218 1 t = 1/ /212 1 Concentration -1 t = 1/217 t = 1/218 1 t = 1/ /212-1 t = 1/217 t 1 = 1/218 t 2 = 1/219 1/212

44 Hypothetical project (for every group): initial cash-flow of 1 M$(5 M$ std dev) per quarter and initial cost to completion of 1 M$ (std dev =.5) Table: Project s value - Panel A: With abandon option Panel B: Without abandon option United States Europe Panel Panel A B A B Launching at t = y (4.5) 39.2 (5.8) 945. (4.8) 64.3 (5.9) Abandon rate 5.77% % - Launching at t = 1y (3.9) 73.2 (5.7) 75.3 (4.2) (5.7) Abandon rate 58.16% % - Launching at t = 2y (4.3) (5.7) (3.6) (5.6) Abandon rate 53.13% % -

45 Hypothetical project (for every group): initial cash-flow of 1 M$(5 M$ std dev) per quarter and initial cost to completion of 1 M$ (std dev =.5) Table: Project s value - Panel A: With abandon option Panel B: Without abandon option EU BigCap EU SmallCap Panel Panel A B A B Launching at t = y (5.3) (6.1) (6.1) (6.6) Abandon rate 37.9% % - Launching at t = 1y (4.5) (5.8) 178. (6.7) (7.1) Abandon rate 45.9% % - Launching at t = 2y (3.6) -1.2 (5.6) (7.1) (7.5) Abandon rate 55.49% % -

46 We have... developed a novel valuation model and methodology to value a (pharmaceutical) R&D project based on real options approach performed simulation analyses considering the interaction ofdifferent external economic and market forces shown that the same project launched in different countries or bydifferent firms (small or large) might have different success and abandon ratesdueto the impact of the economic and industry contexts Our research provides managers with an important tool for timing the introduction of an R&D product to the market.

47 Thank you for your attention!